Lattice Boltzmann Simulation for the Optimized Surface Pattern in a Micro-Channel

Based on the Bhatangar--Gross--Krook (BGK) models, numerical simulation
using the lattice Boltzmann model is performed to investigate the optimized surface pattern in a micro-channel. In order to simulate the practical situation correctly, a slip/no-slip boundary condition is applied with making several assumptions. To assess the validity and efficiency of the model, one benchmark problem with considering the surface patterns is studied. Numerical results show the value of rms velocity V_rms increases with the increasing ratio β and larger Reynolds number Re, higher fluctuation of the rms oscillating velocity. Furthermore, the results show that a good mixing
effect can be obtained when Re is large enough and the ratio β is about 1.618, which is the appropriate choice, i.e. the well known golden section phenomenon.